1.0 Credit

This course includes a thorough study of differentiation and integration with many applications. Limits and continuity are investigated in-depth. The course will emphasize the importance of mathematics studied to date. After completion of this course, the student may wish to take the Advanced Placement Test.

1- Introduction & Review
1- Welcome to Calculus
2- Course Outline
3- Course Syllabus
4- Completing Math Assessments
5- Calculus On The Web
6- Review — Stuff You Should Already Know
7- Pretest
Assignment: Calculus Pretest

2- Limits & Continuity
1- An Introduction to Limits & Continuity
Quiz: Introduction to Limits & Continuity
2- Tangent Lines & Rates of Change
Handout: Tangent Lines & Rates of Change Worksheet
Assignment: Tangent Lines & Rates of Change
3- The Limit
Handout: The Limit Worksheet
Assignment: The Limit
4- One-Sided Limits
Handout: One-Sided Limits Worksheet
Assignment: One-Sided Limits
5- Computing Limits
Handout: Computing Limits Worksheet
Assignment: Computing Limits
6- Infinite Limits
Handout: Infinite Limits Worksheet
Assignment: Infinite Limits
7- Limits at Infinity
Handout: Limits at Infinity Worksheet
Assignment: Limits at Infinity
8- Continuity
Handout: Continuity Worksheet
Assignment: Continuity
9- Additional Resources
Handout: Limits & Continuity Exam
Assignment: Limits & Continuity Exam

3- Derivatives
1- Introduction to Derivatives
3- Definition & Interpretation of the Derivative
Handout: Definition & Interpretation of the Derivative Worksheet
Assignment: Definition & Interpretation of the Derivative
4- Differentiation Formulas
Handout: Differentiation Formulas Worksheet
Assignment: Differentiation Formulas
5- Product & Quotient Rule
Handout: Product & Quotient Rule Worksheet
Assignment: Product & Quotient Rule
6- Derivatives of Trig Functions
Handout: Derivatives of Trig Functions Worksheet
Assignment: Derivatives of Trig Functions
7- Derivatives of Exponential & Logarithm Functions
Handout: Derivatives of Exponential & Logarithm Functions Worksheet
Assignment: Derivatives of Exponential & Logarithm Functions
8- The Chain Rule
Handout: The Chain Rule Worksheet
Assignment: The Chain Rule
9- Implicit Differentiation
Handout: Implicit Differentiation Worksheet
Assignment: Implicit Differentiation
10- Related Rates
Handout: Related Rates Worksheet
Assignment: Related Rates
11- Higher Order Derivatives
Handout: Higher Order Derivatives Worksheet
Assignment: Higher Order Derivatives
12- Additional Resources
Handout: Derivatives Exam
Assignment: Derivatives Exam

4- Applications of Derivatives
1- What’s the Big Deal About Derivatives, Anyway?
2- Rates of Change
3- Critical Points & Extrema
Handout: Critical Points & Extrema Worksheet
Assignment: Critical Points & Extrema
4- The Shape of a Graph
Handout: The Shape of a Graph Worksheet
Assignment: The Shape of a Graph
5- The Mean Value Theorem
Handout: The Mean Value Theorem Worksheet
Assignment: The Mean Value Theorem
6- Optimization
Handout: Optimization Worksheet
Assignment: Optimization
7- Linear Approximations
Handout: Linear Approximations Worksheet
Assignment: Linear Approximations
8- Midtest
Assignment: Calculus Midtest
Handout: Applications of Derivatives
Assignment: Applications of Derivatives

5- Integrals
1- Working Backwards
2- Indefinite Integrals
Handout: Indefinite Integrals Worksheet
Assignment: Indefinite Integrals
3- Computing Indefinite Integrals
Handout: Computing Indefinite Integrals Worksheet
Assignment: Computing Indefinite Integrals
4- Substitution Rule for Indefinite Integrals
Handout: Substitution Rule Worksheet
Assignment: Substitution Rule
5- Area Problem
Handout: Area Problem Worksheet
Assignment: Area Problem
6- Definite Integrals
Handout: Definite Integrals Worksheet
Assignment: Definite Integrals
7- Computing Definite Integrals
Handout: Computing Definite Integrals Worksheet
Assignment: Computing Definite Integrals
8- Substitution Rule for Definite Integrals
Handout: Substitution Rule for Definite Integrals Worksheet
Assignment: Substitution Rule for Definite Integrals
9- Integration by Parts
Handout: Integration by Parts Worksheet
Assignment: Integration by Parts
10- Partial Fractions
Handout: Partial Fractions Worksheet
Assignment: Partial Fractions
11- Improper Integrals
Handout: Improper Integrals Worksheet
Assignment: Improper Integrals
12- Additional Resources
Handout: Integrals Exam
Assignment: Integrals

6- Applications of Integrals
1- What’s the Big Deal About Integrals, Anyway?
2- Area Between Curves
Handout: Area Between Curves Worksheet
Assignment: Area Between Curves
3- Volumes of Solids of Revolution (Part 1)
Handout: Method of Rings Worksheet
Assignment: Method of Rings
4- Volumes of Solids of Revolution (Part 2)
Handout: Method of Cylinders Worksheet
Assignment: Method of Cylinders
5- Volume
6- Work
Handout: Work Worksheet
Assignment: Work
Assignment: Applications of Integrals

7- Sequences & Series
1- Sequences & Series
2- Sequences
3- Series: The Basics
4- Series: Convergence & Divergence
5- Special Series
6- Integral Test
7- Comparison Test
8- Alternating Series Test
9- Absolute Convergence
10- Ratio & Root Tests
11- Strategy for Series
12- Estimating the Value of a Series
13- Power Series
14- Taylor Series
15- Additional Resources
16- Post-Test
Assignment: Sequences & Series

8- Course Survey
Handout: Course Survey
Assignment: Course Survey